Gramian-preserving frequency transformation for linear discrete-time systems using normalized lattice structure

This paper presents a new algorithm for realization of Gramian-preserving frequency transformation for linear discrete-time systems. In the proposed algorithm, we construct allpass systems for frequency transformation as the cascaded normalized lattice structure. It is shown that the frequency transformation based on this algorithm not only leaves the controllability/observability Gramians invariant under the change of magnitude responses, but also significantly reduces nonzero entries of the coefficient matrices of transformed systems. This property will be very effective in practical applications such as implementation of high-accuracy multiband state-space digital Alters.